SOLUTION: Write an equation in point slope form for the perpendicular bisector of the segment with the given end points m(-5,4),N(1,-2)

Algebra ->  Points-lines-and-rays -> SOLUTION: Write an equation in point slope form for the perpendicular bisector of the segment with the given end points m(-5,4),N(1,-2)      Log On


   

Question 960330: Write an equation in point slope form for the perpendicular bisector of the segment with the given end points m(-5,4),N(1,-2)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the equation of the line through the two points.
Find the slope,
m=%28-2-4%29%2F%281-%28-5%29%29=-6%2F6=-1
y-4=-1%28x-%28-5%29%29
y-4=-%28x%2B5%29
y-4=-x-5
y=-x-1
Perpendicular lines have slopes that are negative reciprocals.
m%5Bp%5D=-%281%2F%28-1%29%29=1
y-y%5B0%5D=1%28x-x%5B0%5D%29
y-y%5B0%5D=x-x%5B0%5D
Where x%5B0%5D,y%5B0%5D is a point on the original line.
You can simplify since you know the equation of the original line.
y-%28-x%5B0%5D-1%29=x-x%5B0%5D
y%2Bx%5B0%5D%2B1=x-x%5B0%5D
y%2B1=x-2x%5B0%5D
So now for any value of x%5B0%5D, you know the equation of the perpendicular line.